The equation of states (EOS) of high energy explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) has been studied by using the first principle method. Our results include the lattice constants, elastic constants, and the dependence of total energy and pressure on volume for βand δ-HMX. The calculated elastic constants and the pressure-volume relationship of β-HMX are also compared with the experimental values. The theoretical tensile experiments are implemented on the β-HMX. The atomic-scale analysis displays that the fracture originates from the intermolecule of HMX and is possibly due to the weak interaction of intermolecules.